Martinez has reportedly emerged as Barca's top transfer target, with the LaLiga champion keen to sign a long-term replacement for veteran forward Suarez.
Barca's LaLiga rival Madrid is also reportedly interested, while Premier League giants Manchester United and Manchester City have both been linked.
Inter defender Godin heaped praise on 22-year-old Argentina international Martinez, who had scored 16 goals across all competitions before Serie A was postponed due to the coronavirus pandemic.
"Lautaro is similar to Luis and Sergio Aguero," the Uruguayan centre-back told ESPN.
"He's learning to play using his whole body, with his back to the ball. He's a football player.
"His confidence has a high ceiling and he's maturing with every match. You can spot things in him that tell you he'll be around for 10 or 15 years."
Martinez swapped Racing Club for Inter in 2018 and he has quickly established himself as one of the most sought-after forwards in European football.
He has scored 25 goals in total since joining Inter from Racing Club in Argentina.